This is a phase II, open-label, single centre study of AZD9291 administered orally in patients with advanced lung cancer with activating mutations of EGFR gene with or without T790M which were detected from circulating tumor DNA. EGFR-TKI naïve patients with activating EGFR mutation will be enrolled in cohort 1. Patients with acquired resistance to prior EGFR tyrosine kinase inhibitor (TKI) due to T790M mutation is going to be enrolled in cohort 2.